Let's simplify the given expression step by step:

The given expression is:

$7 - \frac{x - 3}{4} + 2$

Step 1: Combine constants (7 and 2).

$7 + 2 = 9$

So, the expression becomes:

$9 - \frac{x - 3}{4}$

Step 2: Write the expression in a simpler form.

The simplified expression is:

$9 - \frac{x - 3}{4}$

Now, let's compare it with the given options:

• A. $7 - x - \frac{1}{4}$ (Not equivalent)
• B. $x - \frac{3}{4} + 14$ (Not equivalent)
• C. $x - \frac{3}{4} + 9$ (Not equivalent)
• D. $-x - \frac{3}{2} + 14$ (Not equivalent)
• E. $-x - \frac{3}{4} + 9$ (This is equivalent!)

Answer: E. $-x - \frac{3}{4} + 9$

Let me know if you'd like a more detailed breakdown of any step or if you have any other questions!

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Related Questions:

1. How do you simplify similar expressions with fractions and constants?
2. What are the rules for adding and subtracting fractions?
3. Can you explain how to combine like terms in algebraic expressions?
4. How do parentheses affect the order of operations in an expression?
5. What does it mean to simplify an algebraic expression?

Tip:

When simplifying expressions with fractions and constants, always first combine like terms (constants) before dealing with fractions or variables. This reduces errors.